Multiplying Integers
Concept
An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1,908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses. Integers are closed under the operations of addition and multiplication.
The multiplication of integers is one of the basic operations performed on integers. Multiplication of integers is the same as the repetitive addition which means adding an integer a specific number of times.
When we come to the case multiplication of integers, the following cases must be taken into account:
Multiplying 2 positive numbers
Multiplying 2 negative numbers
Multiplying 1 positive and 1 negative number
Rules
1. Multiply the absolute values of the integers.
2. If the two factors have the same sign, the product is positive.
3. If the two factors have different signs, the product is negative.
Example
Multiply.
-7 x -3
Solution
Multiplying 7 and 3 together make 21. Since -7 and -3 are both negative, the product is positive.
So, the answer is 21.
Practice Multiplying Integers
Practice Problem 1
Multiply.
-10 x 4
Practice Problem 2
Multiply.
(-8) ∙ (-5) ∙ (4)2
Practice Problem 3
The price of a car decreases 5 dollars each day. How much value does the car lose in 7 days?
An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.
Positive Integers: An integer is positive if it is greater than zero. Example: 1, 2, 3 . . .
Negative Integers: An integer is negative if it is less than zero. Example: -1, -2, -3 . . .
A zero pair – A pair of the positive and negative form of the same number.
Absolute value – the positive distance that a number is from 0 on a number line.
Additive inverses – two integers that are opposites.
Opposites – two integers that are the same distance from 0 on a number line but in opposite directions, like -5 and 5.
Pre-requisite Skills
Integers and Absolute Value
Order of Operations
Adding Integers
Subtracting Integers